In the light of the several curves on the plate, I am at a loss to see any ground for the support of the view that the Buckeye engine, on account of its steam chest being immersed in wet steam, is necessarily of inferior economy to engines in which the steam chest is stationary and exposed on three sides to the atmosphere. There seems, on the contrary, reason to believe that the wetness of the exhaust steam does not increase the rate of conduction through the surfaces of the main valve sufficiently at most to more than neutralize the advantage in conduction due to the fact that the difference in temperature between live steam inside the valve and the exhaust steam is less than the difference between the live steam and the atmosphere to which four out of five of the surfaces of a stationary rectangular steam chest would be exposed, whereas there is only one such surface in the case of the Buckeye engine.

Referring particularly to the mathematical treatment of the experimental curves, the formulæ of density in terms of the 4ths power of the pressure is a valuable and interesting contribution to that subject. Also, the formula for E, which expresses the experimental water consumption for full stroke cut-off, is a very acceptable method of combining these particular curves. But the method of allowing for the effect of expansion by proposing that the consumption curve at all pressures is a straight line of constant inclination, equal to 22 in 100, is open to the objection that this inclination will vary with different engines in a manner determinable only by experiment. For example, the 7 × 14 Buckeye engine consumption curve has but about one-half this inclination.

If we are to determine the special inclination by experiment for each engine, it becomes a question whether the best use of the experimental curves is not to simply give us a table of values of the per cent. of water unaccounted for by the indicator, which may be applied as a correction to the ordinary calculation of steam consumption. It is doubtful whether it is possible to forecast the water consumption of any engine from data from another size of engine within 2 pounds, in view of the apparently infinite number of conditions upon which the cylinder condensation depends. There is, however, one deduction which seems to follow theory with satisfactory accuracy in all non-condensing engines, viz.: the point of most economical cut-off.

The following table shows this agreement for the case of Mr. Emery's curves. Column 3, calculated for 17 lbs. back pressure,

would average about as much greater than column 4 as it is now below the latter.

The law which here asserts itself represents the controlling influence of the ratio of back pressure to boiler pressure, which never fails to exert an effect proportional to theoretical forecast, in all varieties of steam engines under all practical conditions.

There is one thermodynamic point that I think it proper to mention, and that is regarding the estimation of the cost C. As Mr. Emery states that he expects a dispute on this point, I will not disappoint him. I cannot understand how it is necessary to differ with Mr. Isherwood's method of estimating the value C, if it is estimated at all, and I cannot understand the necessity of estimating its value anyway. I do not see that there is any.

Table showing ratios of expansion for maximum economy, when clearance is five per cent. Engine, non-condensing; Mariotte curve.

c = clearance as a fraction of piston displacement.

=

P1 absolute initial pressure lbs. per sq. inch.

Also, the reference to the experiment of Mr. Barrus on the Dixwell engine does not seem to me any proof of the error of Mr. Isherwood's position, and with 3% possible error of the heat in the condenser, there is very little to be proved at all by the data to which Mr. Emery refers.

Mr. Barrus found that steam at 60 lbs. pressure absolute expanding to double its volume in an engine lost 64 thermal units per pound more than steam which did no work. Therefore the area (Fig. 94) ABCDE=(p1× BC) + p1× BC log 2-14.7 × 144 × AE. Calculation gives ABCD = about 70,000 ft. lbs. and 64 × 772 = about 50,000, and an error of 3% in the total heat determination might make this either 25,000 or 75,000. I append an illustration and argument to sustain my criticism of the cost C.

Let a boiler, Fig. 92, contain a mass of water, A, and of steain, B, at 100 lbs. pressure above zero.

Let a piston, C, form part of the upper surface of the boiler.

Let the area of the piston be 30.8 square inches, so that a resistance of 3,080 lbs. is required to hold the piston in place. Let this resistance be opposed by the atmosphere and the pump piston, D, which is subjected to a head of water, H.

Let the whole of the boiler be felted so as to be without loss of heat. Let the lower half of the boiler have its covering removable, so that it can be immersed in a reservoir of hot oil of sufficient

capacity to cause the evolution of steam described below. Let F be a calorimeter and J a feed pump. We then have i Ca representative of the piston of a non-expansive, non-condensing steam engine.

EXPERIMENT I.

Immerse the boiler in the oil bath to the line aa, and open the cock G, so that steam may flow through it to the calorimeter, F, without altering the pressure in B, and simultaneously let water at 32° be introduced at K, by the pump J, equal in amount to the weight of steam flowing out at G.

When pound of condensed steam has collected in the flask f, close G, and simultaneously withdraw E, and restore the covering to A.

There will have disappeared from E, Q British thermal units. There will be collected in F, Q, British thermal units over the amount represented by the initial temperature of the calorimeter. There will be a thermal units remaining in the lb. of condensed steam in ƒ reckoned above the 32° Fahrenheit. Since the heat contents of the boiler are unchanged it must follow that

Q = Q1 + Q• *

And since the calorimeter F represents Regnault's arrangement for determining the total heat of evaporation of steam, it must follow that Q + q will be 119.19 British thermal units as per Regnault's table.

EXPERIMENT II.

Replace the bath E and let the pressure in B increase an infinitely small amount above 100 lbs., thereby forcing the piston C upward to C-a distance of 2 feet, the pump J supplying water as in Experiment I. Let the bath E be then withdrawn.

To fill the increased space in B caused by the movement of C will require that of a pound of water shall have been evaporated into steam. There will be precisely the same expenditure of heat from E, viz. 119.19 British thermal units, but there will have been allowed to pass outside of B such portion of this heat as is represented by the product of the area of Cx 100 lbs. x the two feet of travel of C.

= =

This work 2 x 100 x 30.8 6,160 foot pounds will have been * This neglects the work done by the pump, J, which being but of one per cent. of the heat of evaporation, is not a necessary element of the discussion.

expended against the atmosphere and the head of water H, so that if the steam in the 2 ft. of space below C' be shut off from connection with the space B, and could all be run into the calorimeter. F, through the cocks d and e, the heat collected in Fand ƒ would 2 x 100 × 30.8 be 119.19 British thermal units.

772

Now, 30.8 sq. inches is 0.214 sq. feet, and 2 × 0.214 sq. feet is the volume of of one pound of steam at 100 lbs. pressure per square inch. Hence the group of figures 2x 100 x 30.8 may be written.

100 × 144 ×°.428

pressure of steam per square foot times

volume of steam to fill cylinder CC in cubic feet.

If therefore ABCD is the indicator card of a non-condensing engine working without expansion, and BE = p1 lbs. per sq. ft.,

Pi

the total heat of evaporation by

1. The useful work is (P1 - 14.7 x 144) V1.

2. The cost of doing the work is Q British thermal units. 3. The heat in the steam at the instant of exhaust is Q-P11, in which p1 is measured to absolute zero.

Consequently, Mr. Emery's quantity C, should be equal to Regnault's total heat, less feed temperature, and his quantity C. if used at all, should be calculated equal to the total forward work, or to absolute vacuum. That is, C1 should be Regnault's total heat, calculated from temperature of feed, and C2 is as per Mr. Isherwood's view, but it is not needed as an element of the cost of the work (P1 14.7) V1.

EXPERIMENT III.

To cover the case of the Barrus test quoted. Suppose an air tight cover at C", Fig. 92, and that the space between C and C' contained of one pound of steam at 100 lbs. pressure. Apply E as